Device for calculating quantitive composition of a substance from an x-ray spectroscopic analysis

ABSTRACT

Two graduated scales, relatively positionable, for making analogue computations of the quantity of a known material in a qualitatively known and quantitatively unknown composition. One scale is calibrated in weight percentages and graduated according to a mathematical function of weight percentages. A second scale is calibrated in units proportional to intensity measurements from an X-ray spectroscopic analysis, and is graduated identically with the first scale.

United States Patent Inventor Donald L. Holden Des Plaiues, Ill.

Appl. No. 734,338

Filed June 4, 1968 Patented Feb. 23, 1971 Assignee Universal OilProducts Company Des Plaines, Ill.

DEVICE FOR CALCULATING QUANTITIVE COMPOSITION OF A SUBSTANCE FROM AN X-RAY SPECTROSCOPIC ANALYSIS 5 Claims, 4 Drawing Figs.

Field of Search [56] References Cited UNITED STATES PATENTS 1,609,97212/1926 Sherrer et a1. 235/70 2,455,522 12/1948 Ringler 235/70X2,773,415 12/1956 Wolfe 235/70X 3,162,363 12/1964 Lavie.... 235/703,282,500 1 H1966 Pikus 235/70 FOREIGN PATENTS 859,063 1/1961 GreatBritain 235/70 Primary Examiner Richard B. Wilkinson AssistantExaminerStanley A. Wal Attorneys-James R. l-loatson, Jr. and Philip T.Liggett ABSTRACT: Two graduated scales, relatively positionable, formaking analogue computations of the quantity of a known material in aqualitatively known and quantitatively unknown composition. One scale iscalibrated in weight percentages and graduated according to amathematical function of weight percentages. A second scale iscalibrated in units proportional to intensity measurements from an X-rayspectroscopic analysis, and is graduated identically with the firstscale.

DEVICE FOR CALCULATING QUANTITIVE COMPOSITION OF A SUBSTANCE FROM ANX-RAY SPECTROSCOPIC ANALYSIS V This invention relates to a device forcalculating the quantity of a material in a composition from an x-rayspectroscopic analysis. More particularly, this invention comprises two,relatively positionable calibrated scales for making analoguecomputations of the quantity of a known material in a qualitativelyknown and quantitatively unknown composition. One scale is calibrated inweight percentages and graduated or scaled according to a mathematicalfunction of weight percentages A second scale is calibrated in unitsproportional to intensity measurement from an X-ray spectroscopicanalysis, and graduated or sealed identically with the first scale.

Heretofore, in deriving the weight percentages of a composite substancefrom the intensity readings of an X-ray spectroscopic analysis, it hasbeen necessary to make arduous and time consuming arithmetic andalgebraic calculations. Besides being vulnerable to manually producedarithmetic errors, the results of such computations are difficult tocompare for different individuals, and for different spectroscopicallyanalyzed substances, even when the computations are performed by thesame individual. This is due to the varying mathematical accuracy of thedifferent methods of computating weight percentages from intensityreadings of an X-ray spectroscopic analysis, and to the varying accuracyof the different formulations used to arrive at the results for thedifferent substances analyzed.

It is an object of this invention to eliminate virtually all arithmeticand algebraic errors in computing-weight percentages from an X-rayspectroscopic analysis. The only source of such an error in using thepresent invention would be in positioning the scales with respect toeach other, or by incorrectly reading figures from the scales. Even ifsuch an error were to occur using this invention, rechecking for such anerror is immensely simplified.

It is a further object of this invention to obtain much more consistentresults than are obtained from manual computations. This advantage isrealized in that with this invention the same mathematical formulationunderlies each result obtained. There is no variation in the degree ofaccuracy, depending upon individual peculiarities in computation, nor isthere any variation in consistency between readings, since variationsarising from rounding off figures or from the use of differentmathematical methods of arrivingat a solution are eliminated. Thepresent invention is appropriate for use wherever it is desired todetermine the percentages by weight of a given material from the X-rayspectroscopic analysis of a qualitatively known, but quantitativelyunknown chemical composition. Thus, this invention will find awidespread application in the quality control of products where thechemical composition is sufficiently critical to warrant an X-rayspectroscopic analysis to insure that the quantities of differentmaterials in such a product stay within certain limits. One such area ofapplication is in the field of catalyst production. Another area of useis in the refining of metals and the productions of steel and othermetal alloys, particularly where additives are used to enhance certainproperties. Other appropriate areas are in electroplating and inrefiningand blending petroleum products.

In a broad aspect this invention is a device for calculating thequantity of a known material, in a' substance having a known qualitativeand an unknown quantitative chemical composition, from the intensitymeasurement of an X-ray spectroscopic analysis of said substance,comprising two relatively movable members, the first of said members.having scales calibrated in weight percentages and scaled according tothe logarithm of the quotient of said weight percentage divided by lminus said weight percentage, and the second of said members havingscales calibrated in values directly proportional to said intensitymeasurement and scaled identically with the scales of said first member,and reference values for a chemical composition qualitatively identicalto the aforesaid substance are indicated on at least one of said scalesof said members, whereby the scales of the aforesaid members arealignable according to said reference values, and the percentagecomposition for the aforesaid known material is determinable from thevalue directly proportional to intensity measurement for the aforesaidsubstance.

In an X-ray spectroscopic analysis, the substance, or sample to beanalyzed is mounted in a sample cup or cell and is bombarded withpolychromatic X-rays or X-rays of a given wave length. In the proceduredescribed, the samples are considered to be infinitely thick" toX-rays.The actual sample thickness of one-fourth to one-half inch is such as toallow less than 1 percent of the total X-rays to completely penetratethe sample. Upon striking the substance, the exciting X-rays displaceelectrons from the inner orbitals of the molecules comprising thesubstance. As these vacancies are filled with other electrons, energy inthe form of X-rays, characteristic of the particular molecule areemitted. This polychromatic radiation from the sample is resolved byusing a single crystal such as lithium fluoride for a grating. Eachcharacteristic X-ray line therefore appears at its expected position onthe goniometer circle where it may be detected and measured in intensityby a proportional, or scintillation, or other counter. Normally, theelements comprising the substance analyzed are known prior to thespectroscopic analysis. The spectroscopic analysis is conducted for thepurposeof making quantitative determinations of one or more of theelements present in a substance. The quantity of an element present canbe determined from the intensity of one of its characteristic X-raylines. Where the concentration for a particular element is less thanabout 0.3 percent, the concentration is usually directly proportional tothe intensity of the characteristic X-ray line for that element. Whereconcentration of an element increases beyond 0.3 percent, the absorptioneffects of this element and the other elements increasingly affect theintensity of the reflected X-rays. The effect of this absorption can beseen from the equation which may be used to compute weight percentagefor a specific element while correcting for the absorption effects. Thisequation may be expressed as follows for samples which may be consideredinfinitely thick:

where C is the weight percentage to be calculated of an element; C 6,,etc., are the weight percentages of the other elements of the substance(the sample matrix); and a a etc., are the ratios of the X-ray massabsorption coefficient of the other elements to that of the elementbeing calculated. 1,, is the intensity of the characteristic X-ray linefrom the pure element for which the weight percentage is being sought. 1is the measured intensity for the substance analyzed. In the aboveexpressions, the products of the absorption ratios and the weightpercentages of the other elements can be combined to form anotherexpression:

In this expression, A is the effective absorption coefficient of thematrix or other elements. The word effective" is used to describe Asince the true value of A may not always be equal to the summation ofthe individual absorption coefficients, due to the enhancing effect ofcertain elements in the substance analyzed. These effects may change thevalue of A somewhat, for different concentrations of the material beinganalyzed. For this reason, the selection of appropriate reference valueson the scales, as will be described herein, is important.

The aforesaid equation may be further modified by rearranging theequation and substituting the term R, which is equal to I X IO0/l,,, inthe rearranged equation thus forming the expression:

which can be expressed as It can be seen that the logarithms of thefunction of weight percentage and intensity differ only by log A. Ifalignable scales are graduatedv or sealed according to the logarithms ofthe two functions, that is, if the scales are calibrated according tothe variables and if a set or corresponding values of the two functionsis known as a reference, either variable can be determined from thescales, when the other variable is given. The present invention utilizesthis relationship to facilitate the computation of weight concentrationwhen the variable R, as derived from the intensity measurement of theX-ray spectroscopic analysis, is known.

The present invention has a first member, with scales graduatedaccording to the values of the logarithm of the aforesaid function ofweight percentage, and calibrated according to the variable itself. Thatis, the scales are linearly disposed according to the values of thelogarithm of the function C/( 100-), and the values of C are indicatedat appropriate points on the scales. This invention also has a secondmember with the scales graduated according to the logarithm of theaforesaid function of intensity, that is, according to thelogarithm ofthe function R/( 100-). The values of R are indicated at the appropriatepoints on the scales on this second member. Since the two functionsinvolved are mathematically identical except for the variables R and Cscaling of said first member will beidentical to that of said secondmember, thus the distance between two numerical values of the variableon one scale will equal the distance between the same numerical valuesof the variable on the other scale.

To facilitate computations, proper alignment of the scales must beaccomplished with relative case. One manner of obtaining this result isthrough exterior tables of reference values, that is, correspondingvalues of the variables from previous calculations obtained from X-rayspectroscopic analyses of standards comprised of the same elements asare the quantitatively unknown substances under investigation. Forexample, where previously a standard of silica and nickel has undergonean X-ray spectroscopic analysis, it can be determined that for a knownnickel concentration of 5.95 percent an intensity will be obtained suchthat R is equal to 20. In determining the nickel concentration in futuresamples consisting of silica and nickel, the scales need merely bealigned so that the value of C (5.95) on the scales of the first memberis directly opposite the value of R (20) on the scales of the secondmember. The nickel concentration in each future sample need merely beread from the scales of the first member opposite the new values of R onthe scales of the second member. As previously noted, it is preferableto choose the reference values used as near as possible to theconcentrations being determined. In this manner, errors from variationsin the absorption coefficient are minimized due to alteration of thematrix, since changes are negligible over small ranges of composition.An unusual sample having a wide deviation in concentrations from thenormal should receive special treatment to reduce possible inaccuracies,since the effective absorption coefficient of its matrix maybematerially different from that of the normal sample. Such'sp'ecialtreatment may include diluting the sample with'a standard matrix such assilica or water, or applying mathematical corrections to the absorptioncoefficient of the matrix using literature values of mass absorptionCOEffiCIQBI'IIS. 1

Rather than using exterior tables for reference values, it is oftenpractical, when X-ray spectroscopic analyses are frequently performed'onsubstances containing the same elements, to conspicuously indicate thereference values of the variables on the scales themselves. Referencingthe scales in this manner perfonns the same function as do exteriortables of reference values. In both cases, alignment of the members ofthis invention for calculating the quantity of known materials insubstances analyzed is accomplished.

The inscribed calibrations on each member may all be made on a singlescale, or they may be divided into as many scales as desired, dependingupon the accuracy desired and the physical length to which it is desiredto limit any one member.

The preferred embodiment of this invention is constructed much the sameas is a common bar slide rule. In this embodiment, the scales of percentconcentration are parallel to each other along the length of a firstmember, which is comprised of two parallel components, and of transversebraces which fasten the ends of said parallel components together, saidcomponents having tracks on their inner edges to engage and linearlyrestrain a second member. Said second member is comprised of a singlecomponent having complimentary lips to engage the tracks of said firstmember. Said second member fits slideably between the components of saidfirst member so that the two members are always parallel and areslideably alignable. The reading of corresponding values from the scalesmay be further facilitated by the addition of a transparent third membercontaining a crosshair perpendicular to the scales on the first andsecond members, and which fits slideably around the aforesaid first andsecond members. The crosshair may be centered on the appropriate valueof the function of intensity, and the crosshair will then define thecorresponding percent concentration. The scales of said first and secondmembers may be on one side, or on both sides of their respectivemembers.

Another embodiment of this invention has a construction similar to thatof a disc slide rule. In this instance the first member is a planar discand the second member is a smaller planar disc, both discs being mountedtogether about the same axis, both discs having the aforesaid scales inthe form of concentric circles inscribed thereon, the smallestconcentric circle of said first disc having a greater diameter than thediameter of said second member. The incorporation of a transparent thirdmember mounted about the same axis and having a radial crosshair tofacilitate alignment, is also appropriate to this embodiment.

Another embodiment of this invention is a construction similar to thatof a cylindrical slide rule, wherein the first member is a cylinder withretaining means on its ends, and said second member is an annularsleeve, fitting slideably around said first member and retained on saidfirst member by the aforesaid retaining means, and the aforesaid scalesare inscribed in the form of rings about the respective members and arespaced parallel along the surfaces of the respective members.

The simplest of all embodiments is where said first member issubstantially a planar surface with scales extending lengthwise on thesurface of said first member and said second member is further comprisedof an elongated single component with the aforesaid calibrations on saidscales of said second member inscribed on all sides and on all linearedges parallel to the length of said component. In this case, the planarsurface may merely be a sheet of paper. This embodiment is of particularadvantage when the X-ray spectroscopic analyses are performed on anumber of substances made up of different elements, since a number ofdifferent sheets of paper with percentage concentrations scales can beused with appropriate reference values thereon. This avoids placing alarge number of reference marks on a single concentration scale or on asingle sheet of paper. In this manner, the second member will have noreference marks on it, while the various sheets of paper have indicatedreference percentage concentrations and also references to thecorresponding readings on the second member, for each substanceanalyzed.

The various features of the preferred embodiment of this invention arefurther illustrated in the accompanying drawings in which:

FIG. 1 is a view of the front surface of the preferred embodiment ofthis invention;

FIG. 2 is a view of the rear surface of the preferred embodiment of thisinvention;

FIG. 3 is an end view of the preferred embodiment: and

5" FIG. 4 is an enlarged view of the upper right-hand portion of thesurfaces of adjacent first and second members in F l0. 2.

Referring now to the drawings, a and a are two parallel components of afirst member of the invention. Transverse braces c and d fasten the endsof components a and a together. Screws h fasten the braces to componenta and rivets e fasten the braces to component Components a and a eachhave a track f on their inner edges to engage and linearly restrain asecond member b. The second member is comprised of a single component bwhich has lips g on each of its outside edges. Lips g are complementaryto and engage tracks f, whereby member b fits slideably'be'tweencomponents a and a. A transparent third member a fits slideably aroundthe components a and 0, thereby enclosing member b. Thus, member bslides along tracks f on the inside edges of components a and a parallelto components a and a, and third member u slides along the outside ofand parallel to components a and a. Third number 14 has a crosshair vwhich is perpendicular to the direction of movement of the third memberu and which is also perpendicular to the scales on components a and a.

Duplicate scales i are located near the outside edges of the front ofcomponent a and the rear, or back of component a. Duplicate scales k areon the inside edge of the front of component a and on the inside edge ofthe back of component a. Duplicate scales j are parallel to and locatedbetween scales i and k, both on the front of component a and on the backof component a. Duplicate scales n are near the outside edge of thefront of component a and the outside edge of the back of component a.Duplicate scales 1 are on the inside edge of the front of component aand the inside edge of the back of component a. Duplicate scales m areparallel to and located between scales 1 and n, both on the front ofcomponent of a and on the back of component a. Thus, two complete setsof scales i, j, k, l, m, and it exist, one on the front of said-firstmember and one on the rear of said first member. While duplicate scaleson said first member are not essential to the operation of thisinvention, they facilitate alignment of said first member with saidsecond member.

The set of scales i, j, k, l, m, and n on the front of the first memberand the duplicate set of scales i, j,-k, I, m, and n on the back of thefirst member are graduated according to the logarithm of the functionC/( 100 and are calibrated according to values of C, where C is theweight percentage. Together each set of scales covers the range ofvalues of the function of C from C equals 0.012 to C equals 96. Sincethe logarithm of this function approaches infinity as C increases, it isnot possible to cover the entire range of the function. Each scale i iscalibrated from C equals 0.012 to C equals 0.15, and each scale j iscalibrated from C equals 0.15 to C equals 1. Each scale k is calibratedfrom C equals 0.8 to C equals 6, while each scale I is calibrated fromCequals 5 to C equals 30. Each scale m is calibrated from C equals 30 toC equals 75, and each scale n is calibrated from C equals 75 to Cequals96.

On the front of member b are two scales. Scale 0 is on the front ofmember b at the edge adjacent to scale k on component a, and scale p ison the front of component b at the edge adjacent to scale I on component0'. Scale q is on the rear of member b at the edge adjacent to scale kon component a While scale r is on the rear of member b at the edgeadjacent to scale I on component 0. These scales, 0, p, q, and r, arenot duplicated on member b as are the scales on components a and a.Scales o, p, q, and r, are graduated according to the logarithm of thefunction R/( 100-), and are calibrated according to values of R.Together these scales cover the range of values of the function of Rfrom 0.25 to 83. Since the logarithm of this function approachesinfinity as R increases, and negative infinity as R decreases, it is notpossible to cover the entire range of the function. Scale 0 iscalibrated from R equals 0.025 to R equals 0.29, and scale p iscalibrated from R equals 0.29 to R equals 3.4. Scale q is calibratedfrom R equals 3.4 to R equals 30, while scale ris calibrated from Requals 30 to R equals 83.

' known for R, the function of intensity,

It can be seen that if corresponding reference values are and for C, theweight percentage concentration, for a substance comprised of particularelements, the weight percentage concentration can be easily found fromthe measured intensity for any subsequent samples analyzed by X-rayspectroscopy, where the samples contain the same elements as theaforesaid substance. As illustrated in H6. 4, corresponding referencevalues are conspicuously indicated on the scales of the invention forsubstances which are frequently analyzed by X-ray spectroscopy.Reference values for a substance comprised of nickel and alumina (A1 0,)and for a substance comprised of nickel and silica (Si0 are inscribed at.r l and p respectively. At .r, a reference point for weightconcentration of nickel in alumina, the corresponding reference valuefor R, the function of intensity, is indicated. This value, asillustrated, is 20, and is followed by the composition of the substance,Ni Al,0,, and a line leading to the reference point for weightconcentration on the scales of components a and a. This reference pointis 5.15 on scale k on component a. At t, a reference point for weightconcentration of nickel in silica, the corresponding reference value forR, the function of intensity, is indicated. As illustrated, this valueis 20, and is followed by the composition of the substance, Ni Si0,, anda line leading to the reference point for weight concentration on thescales of components a and a. This reference point is 5.95 on scale k oncomponent a.

If it is desired to determine the weight percentage of nickel in asubsequent sample of nickel in alumina, where the computed value of R,according to the definition of R, is 10, is aligned with components aand a according to the reference values for nickel and alumina. That is,scale k, at C equals 5.15, is positioned opposite scale q at R equals20. Crosshair v is aligned along member b at the point on scale q whereR equals 10, and the weight percentage of nickel can be determined fromthe intersection of crosshair v with scale It on component a. Morespecifically, as illustrated, the weight percentage for a sample ofnickel in alumina having a value of R equal to 10, is 2.33.

The embodiment as illustrated in the drawings is not to be construed aslimiting the different devices upon which the aforesaid scales can beplaced. Although possible devices which may serve as the physicalembodiments of this invention include those means which are commonlyemployed in slide rules, this invention is not to be considered limitedthereto.

lclaim:

l. A device for calculating the quantity of a known material, in asubstance having a known qualitative and unknown quantitative chemicalcomposition, from the intensity measurement of an X-ray spectroscopicanalysis of said substance, comprising two relatively movable members,the first of said members having a plurality of parallel scales disposedthereon calibrated in weight percentages and scaled according to thelogarithm of the quotient of said weight percentage divided by minussaid weight percentage,'each one of said plurality of scales on saidfirst member covering a distinct predetermined range of values of saidweight percentages, and the second of said members having a plurality ofparallel scales disposed thereon calibrated in values directlyproportional to said intensity measurement and scaled with the distancesbetween values on the scales of said second member equal to thedistances between the same values on the scales of said first member,each one of said plurality of scales on said second member covering adistinct predetermined range of values of said intensity measurements,and reference values for a chemical composition qualitatively identicalto the aforesaid substance are indicated on at least one of said scalesof said members, whereby the scales of the aforesaid members arealignable according to said reference values, and the percentagecomposition for the aforesaid known material is determinable from thevalue directly proportional to intensity measurement for the aforesaidsubstance.

2. The apparatus of claim 1 furthercharacterized in that correspondingreference values are conspicuously indicated on said scales forsubstances which are frequently analyzed by X-ray spectroscopy, herebyfacilitating alignment of said members for calculating the quantity ofknown materials in said substance.

3. The apparatus of claim 1 further characterized in that thecalibration of percentages on said scales of said first member coversthe range of values from 0.012 to 96 and the calibration of intensitymeasurements on said scales of said second member covers the range ofvalues from 0.025 to 83.

4. The apparatus of claim 4 further characterized in that said firstmember is further comprised of two parallel components, and transversebraces which fasten the ends of said parallel components together, saidcomponents having tracks on their inner edges to engage and linearlyrestrain said s second member; said second member is further comprisedof a single component having complementary lips to engage the tracks ofsaid firstmember, and fitting slideably between the components of saidfirst member, and in addition a trans-

1. A device for calculating the quantity of a known material, in asubstance having a known qualitative and unknown quantitative chemicalcomposition, from the intensity measurement of an X-ray spectroscopicanalysis of said substance, comprising two relatively movable members,the first of said members having a plurality of parallel scales disposedthereon calibrated in weight percentages and scaled according to thelogarithm of the quotient of said weight percentage divided by 100 minussaid weight percentage, each one of said plurality of scales on saidfirst member covering a distinct predetermined range of values of saidweight percentages, and the second of said members having a plurality ofparallel scales disposed thereon calibrated in values directlyproportional to said intensity measurement and scaled with the distancesbetween values on the scales of said second member equal to thedistances between the same values on the scales of said first member,each one of said plurality of scales on said second member covering adistinct predetermined range of values of said intensity measurements,and reference values for a chemical composition qualitatively identicalto the aforesaid substance are indicated on at least one of said scalesof said members, whereby the scales of the aforesaid members arealignable according to said reference values, and the percentagecomposition for the aforesaid known material is determinable from thevalue directly proportional to intensity measurement for the aforesaidsubstance.
 2. The apparatus of claim 1 further characterized in thatcorresponding reference values are conspicuously indicated on saidscales for substances which are frequently analyzed by X-rayspectroscopy, thereby facilitating alIgnment of said members forcalculating the quantity of known materials in said substance.
 3. Theapparatus of claim 1 further characterized in that the calibration ofpercentages on said scales of said first member covers the range ofvalues from 0.012 to 96 and the calibration of intensity measurements onsaid scales of said second member covers the range of values from 0.025to
 83. 4. The apparatus of claim 4 further characterized in that saidfirst member is further comprised of two parallel components, andtransverse braces which fasten the ends of said parallel componentstogether, said components having tracks on their inner edges to engageand linearly restrain said second member; said second member is furthercomprised of a single component having complementary lips to engage thetracks of said first member, and fitting slideably between thecomponents of said first member, and in addition a transparent thirdmember containing a crosshair perpendicular to the scales of said firstand second members, fits slideably around the aforesaid first and secondmembers.
 5. The apparatus of claim 1 further characterized in that saidfirst member is substantially a planar surface with said scalesextending lengthwise on the surface of said first member and said secondmember is further comprised of an elongated single component with theaforesaid calibrations on said scales of said second member inscribed onall sides and on all linear edges parallel to the length of saidcomponent.